The breakdown of helium, produced by single-mode laser beam with a triangular time-variation, has been calculated on the basis of the cascade mechanism by following the evolution of the electron energy distribution. A simple model of the helium atom has been used-a ground state, one excited and one ionised state, and the collision cross-sections for ionisation, excitation, and ionisation of the excited state have been taken from the literature. With parameters corresponding to a focal spot of diameter 14 mu m, in helium of pressure between one and 12 atm, and no loss processes, the computed breakdown threshold intensities were found to be within a factor of two of those determined experimentally. On making allowance for diffusion losses, the agreement improved to the order of 20%.